You children are school aged so an option may be some services the school can offer you to help things. the school psychologist will also know of community services that can also help you.

The DHS agency here when I became depressed and suicidal has a temporary foster care program where the children are in care for up to a year so that the parents can get things together mentally. With their help my son and I were able to jump to the top of all the waiting lists and get into individual and family therapy. the catch is that here in this state you only have a year, after that the temporary placement become permanent. Also If you go that route beware though foster care system is not ideal. My son came home with what I was told was reactive attachment disorder. We now know he isn't RAD he most likely has schizophrenia so even if he hadn't gone into foster care he would have eventually become as unstable as he is. But it didn't help matters him seeing me go over the edge. He now has PTSD in part from my becoming and acting depressed and suicidal in front of him.

Only you can decide if you should give up your children and at the very least it might help for you to discuss your options with a therapist that way if you do give them up you are not making the decision in the heat of the moment but have looked at all sides of the problem and options. Good luck.